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One Sample Variance Test
What do you know about the one-sample variance test? Did you know that, unlike many other tests, it is not very robust for non-normal data? What does "not very robust" mean?
In the example shown here, the test accepts the null hypothesis that the variance is equal to the known population variance less than 84% of the time. When you run the test, you are assuming a 95% rate of acceptance. The distribution used in the simulation is highly skewed - as a result there is a greater chance of obtaining large sample variances than there would be if you sampled from a normal distribution. This causes the acceptance rate to drop, as seen here. You need to be very careful when using this test for non-normal data - the reported p values from the test could be severely underestimated.
We have developed a macro that allows you to check the acceptance rate for various degrees of skew, with a target sample size, and modify the number of samples used in the simulation. The default here is 10,000 samples for each designated sample size.
|One-sample t test simulation|
|Wilcoxon test simulation|